NEET UG 2021 — Thermodynamics

In an adiabatic process

Match Column - I and Column - II and choose the correct match from the given choices. <table class="pyq-table"><tbody><tr><td>Column - I</td><td>Column - II</td></tr><tr><td>(A) Root mean square speed of gas molecules</td><td>$(P)\frac{1}{3}nm{v}^{2}$</td></tr><tr><td>(B) Pressure exerted by ideal gas</td><td>$(Q)\sqrt{\frac{3RT}{M}}$</td></tr><tr><td>(C) Average kinetic energy of a molecule</td><td>$(R)\frac{5}{2}RT$</td></tr><tr><td>(D) Total internal energy of $1\mathrm{mol}$ of a diatomic gas</td><td>$(S)\frac{3}{2}{k}_{B}T$</td></tr></tbody></table>

A cup of coffee cools from $90^{\circ}C$ to $80^{\circ}C$ in $t\mathrm{min}$, when the room temperature is $20^{\circ}C$. The time taken by a similar cup of coffee to cool from $80^{\circ}C\text{to}60^{\circ}C$ at a room temperature same at $20^{\circ}C$ is :